signextension

Sign extension is the process of increasing the bit width of a binary signed integer while preserving its numerical value. In two's complement representation, this is accomplished by replicating the most significant bit (the sign bit) into all newly added higher-order bits. Sign extension contrasts with zero extension, which fills new bits with zeros and only preserves the value for unsigned numbers.

In practice, sign extension occurs when promoting a smaller signed integer to a larger width, such as converting an 8-bit value to 16- or 32-bit. Most architectures provide an instruction or operation to perform sign extension automatically, for example MOVSX on x86 (move with sign-extend), or similar instructions on ARM and other processors. Compilers also insert sign-extension logic when evaluating expressions that mix signed integers of different widths.

Examples: If the 8-bit value is 0x7F (binary 01111111), sign extension to 16 bits yields 0x007F. If the 8-bit value is 0x80 (binary 10000000), sign extension to 16 bits yields 0xFF80, which represents -128 in signed 16-bit two's complement. The operation preserves the signed value, not the bit pattern, across width changes.

Sign extension is essential in arithmetic, memory access, and language semantics. When reading a signed value from a byte, a register transfer, or converting between types in programming languages, incorrect sign extension can change the interpreted value. Understanding sign extension helps ensure correct behavior in low-level code, compilers, and data serialization across varying bit widths.